this will probably start a war lol
#book-recommendations
narrow dragon
sage python
It was only in 4th year that that my algebra started catching up to my functional analysis lmao
marble solar
The main purpose of every field that is not analysis is to strive to be analysis
sage python
Even now I'd say what I do is in the middle of the two, automorphic forms
robust palm
@narrow dragon do you have a pdf of davenport's book or did you buy the ebook or a physical copy
narrow dragon
I used to use the one in the university library
now I just use my old friend libgen
🙂
robust palm
I just downloaded it, will definitely take a look
narrow dragon
I hope you enjoy it!
sage python
Analytic NT squad
civic carbon
Overholt is probably my favorite
quick hornet
Escaping the Cult
limpid gazelle
civic carbon
there is a slightly "friendlier" one that I like whose name I now cannot remember
sage python
I haven't seen much analytic NT in the sense of like, prime number theorem and all, including this book
Right now I'm reading Diamond-Shurman but generally my main thing atm is Goldfeld-Hundley
Modular/automorphic forms
civic carbon
Konnick and Luca that's the other one
limpid gazelle
Ok I'll check those out
civic carbon
I do not like these books treatments of the proof of PNT, but I like them overall.
limpid gazelle
Apparently his name is Koninck btw
civic carbon
It seems to me that most analytic number theory texts try to minimize the amount of complex analysis needed, and that is wholly the wrong approach for a subject based on complex analysis imo
damn my dyslexia 😛
sage python
Yeah you'll wanna know it for the most part with zeta stuff
civic carbon
well, PNT is "zeta stuff" and so is Dirichlet's theorem, imo. There is plenty of analytic number theory you can do with just calculus II basically, of course.
long bear
basel problem part 2 when
sage python
Yeah, I just mean that like, stuff involving the zeta function, aka a lot of stuff, you want complex analysis for
quick hornet
half of math is zeta stuff, the other half is good
sage python
ur mom is a zeta stuff
quick hornet
damn you got me
civic carbon
haha Basel Problem Part 2 in a couple weeks. Everything is done except animations of algebra.
sage python
Nice
long bear
epic
sage python
Basel problem is the pi^2/6 thing?
long bear
yeah
dapper root
Lmao
trail tusk
True mathematicians don’t worry about convergence
civic carbon
I promise I will not say any words about convergence in the video
but I show how to calculate zeta(2k) for all k in terms of the Bernoulli numbers, and also talk about Riemann's explicit formula for Psi(x) in terms of the zeroes of zeta
trail tusk
Channel link?
granite ferry
oh is this actually you @civic carbon ?
fathom monolith
civic carbon
Yes it is me
long bear
the next 3b1b
dense pewter
3zeta1math
long bear
rainbow pupil
sturdy copper
what are some of the recommended texts in the realm of topology? in particular, ones that might be good for studying in parallel with special/general relativity?
I come from the perspective of having dropped out of an EE degree before getting past calc 2, and I've been picking my way through the first few chapters of Carrroll's GR book, backtracking here and there (mostly with Wikipedia) to fill in some gaps on concepts like manifolds, metrics and the Lorentz transform, a little bit of vector/field differentiation (though that's mostly unrelated to what I'm asking about), and I've found myself more interested in the math concepts than the applications to cosmology
gray gazelle
https://www.amazon.ca/Semi-Riemannian-Geometry-Applications-Relativity-Barrett/dp/0125267401
a phd student in the field recommended this one to me, might be worth looking at
if by "topology" you mean moreso point-set stuff, munkres is usually recommended
sturdy copper
I'm not quite sure what I mean, in all honesty, but I'll look into it
thank you!
O'Neill looks like it's close to what I want, at least to start
tribal kernel
Honestly Lee’s trilogy of GTM books on manifolds are all really easy to read and present material clearly. The final book on Riemannian manifolds is particularly applicable to relativity studies. Munkres is also a good start for intro topology. It’s gives clear if dry ways of characterizing topological spaces.
gray gazelle
second the lee recommendations, those books are great
tribal kernel
Here’s the link to the Riemannian manifolds book. Technically this is a bit more geometry than topology but it’s stuff that is super relevant to GR.
Yeah and I used all three of them in my undergrad geometry classes! Very nice texts!
normal sandal
what's a good textbook for complex analysis? I currently have Complex Analysis Third Edition by Joseph Bak and Donald J. Newman, which is a pretty decent textbook I feel, but it's not very clear sometimes.
gray gazelle
can I ask for a solution manual here?
brittle latch
never ask to ask for something just ask for it straight away and if somebody can comply they will
sturdy copper
@tribal kernel thank you, too!!
gray gazelle
(Duxbury Advanced) John A. Rice - Mathematical Statistics and Data Analysis 3ed (Duxbury Advanced) -Duxbury Press (2006)
Anyone has the Solution manual for this book?
marble rock
is the topology in rudin good enough for a topology course?
i am really super lazy in leanring both analysis and topology but those are mandatory to take in uni
so i am trying to take the most shortcut ever
marble solar
No it is not good enough for a general point set topology class
Usually you use a text like Munkres
There's a lot of interesting and often useful facts that it doesn't cover
stray veldt
does munkres cover filters or nets?
tribal kernel
Yeah the topology that’s done in my analysis books is focused on metric spaces primarily. So if you want to learn general topology, an analysis text usually isn’t the way to go. There are likely exceptions of course
Let me check. I think it covers nets
marble rock
i dont get it
both of them are boring as fuckand both them u need for each other
like i dont get why learning top without analysis is bad
and when u learn analysis u learn top but its useless?
why
do i have to read both rudin and munkres
marble solar
No munkres doesn't cover filters & nets
marble rock
rudin is hard for me
marble solar
You don't have to read either
marble solar
There is no royal road to real analysis
stray veldt
how does it prove tychonoff without filters
limpid gazelle
@marble rock wdym? analysis and topology are both interesting
marble rock
thats subjective ig
and i dont know much about math in general so my opinion would be wrong yea
but im just saying on how i feel
saying*
stray veldt
rudin probably covers the most results in the least space
stray veldt
there are shorter top books than munkres though
marble rock
yea like what
stray veldt
that get you up to speed
stray veldt
i like waldmann
marble rock
some1 recommedned me
stray veldt
but im biased because i know the guy
marble rock
hatchers notes
and they are ilke 30 pages
or 50
but i am afraidi they arent good enough for someone with 0 knowledge
waldmann
okay but for analysis
whats fast text
marble rock
other than rudin ;D
tribal kernel
It’s not that topology learned in analysis is useless. It’s just not usually geared towards talking about topology in R^n or infinite dimensional vector spaces. Just most specific
Rudin is a really difficult analysis text
marble rock
dense?
limpid gazelle
I feel like if you jump straight to general topology without analysis it will be a bit difficult and abstract
marble rock
oh my god
ddid i click on the wong text?
why is there a gropus adn rings and fields
in the textbook
stray veldt
which?
marble rock
yours
stray veldt
you can skip that
marble rock
vec spaces affine spaces?
stray veldt
it just introduces everything it needs
marble rock
lmlfaao
tribal kernel
Marsden and Hoffman is my favorite classical analysis book. Folland’s text and Royden’s text are really good modern analysis texts
marble rock
weird af form e
stray veldt
its a 3 book series
stray veldt
for analysis? no
marble solar
I wouldn't be focused on getting through things quickly
marble rock
i want something to be dense
in the same sesne loch said
im going to read analysis after a few chaps of AM
marble solar
Rudin is dense
tribal kernel
Friedman’s Modern Analysis is good and short
marble rock
i dont like rudin
stray veldt
max recently recommended a new topology book
sage python
Lol I think you're asking for a lot
marble rock
i couldnt find it
marble solar
Cat. Theory is a meme
marble rock
topology and category theory
tribal kernel
Rudin is good but it’s incredibly dense and hard to follow if you’re not 100% with him
marble rock
@sage python analysis textbook other than rudin that isnt slow as tao?
stray veldt
but waldmann is also less than 150 pages and i like it
sage python
Probably Pugh, there's also one by Igor Kriz
tribal kernel
Kolmogorov also has a good short analysis book
sage python
But yeah mo2men you gotta just accept that like
Math doesn't have a clean path where you can do exactly what gives you enjoyment
sage python
At some point, in fact at many, you'll have to swallow it and be like
This is what it takes to git gud
marble rock
i am doing it cuz
uni is coming
andd theres a very big chance iam going to do math at uni
and if that happens
i am goign to have to yea swallow
tribal kernel
What kind of uni?
marble rock
normal uni?
tribal kernel
Like what major?
marble rock
math
tribal kernel
Undergrad?
sage python
I mean you can continue in algebra if you're waiting until an analysis class to do analysis but you're gonna need to tone things down
sage python
From what I've seen you're not really there yet for Atiyah-Macdonald
stray veldt
there is a reason
tribal kernel
Ah are you comfortable with classical analysis?
marble rock
yea i am going to take alot of time with atiyah mcdonald
rereading and redoing problems
i was sorta fine with df
maybe you were right but meh
sage python
You need to focus on earlier things first, do most of DF's ring theory
marble solar
I think Rudin takes about a year to absorb
sage python
Hmmm
marble solar
At a basic level
marble rock
its just that the problems ind f
tribal kernel
Cause if you aren’t, Marsden and Hoffman’s book is really good for undergrad analysis.
sage python
That's a bit much idk
marble rock
once u get to the later probs things get a bit harder which is cool
sage python
My class got through most of it in about 10 weeks
sage python
Chapters 1-7 and 9
marble rock
i should have learnt analysis waaaaaay back
so i be able to solve eproblems
but meh
sage python
Thing is we had quite a lot of problems on our psets lol
marble solar
You're just going for the sake of being done, the ideas won't stick at that pace
sage python
Like one week was 2/3 of the problems in chapter 9 sorta thing lmao
tribal kernel
Munroe’s book on integration is pretty simple and good too. Good introduction to measure theory
sage python
I mean idk for me it largely worked somehow. I guess our prof felt most of chapters 1 and 3 we should've known from calc
marble rock
i'll be back when i finish localization in AM
and then im done with algebra
problem is i didnt know u had to look at a problem for an hour to find it solution
marble rock
like i would jjust look at it for 3 mins and if i cant get it its done
this will take me so much time
marble solar
Throws all pedagogy out the window
marble rock
ur lvl of math not same of mine ig haah
sage python
The first n problems in DF tend to be fairly straightforward anyway, even within DF a bunch of them will be taking a lot longer
sage python
Thing is that book has like, 40 problems per section
marble rock
u get to see alot of theory building
sage python
And the first 15 of them are instant
marble rock
and alot of hard shit
like the limits one this 1 fucked me baddd
me seeing limits for the first time
insta run
stray veldt
i would be doing the first 15 problems "yea this is easy" and skip the rest, lmao
marble rock
yea thats me
sage python
Moonbears: So I guess my overall take on that class was, definitely a lot of things could be done better but
Like we had stuff on top of just Rudin, and it put a lot of demands on our time
stray veldt
but like, i didnt self study until i knew a fair bit of mathematics already
sage python
Like multiple weeks I'd spend over 35 hours on the pset and not finish or look things up
marble rock
should i stop AM after modules?
sage python
But this wasn't a byproduct of just the speed that we'd go through Rudin
We also had to teach ourselves linear algebra
marble rock
if i do that i would have learnt everything in a normal course in alg
sage python
And the lectures were not great because the prof wasn't good at recovering after mistakes
marble rock
groups rings fields modules vec spaces ig
stray veldt
imagine doing mistakes
sage python
And was generally kind of a mess
stray veldt
my linalg (and number theory prof) did mistakes all the time
and then went back and corrected them with red chalk
quartz pawn
lol.
marble rock
mistakes in like whaT?
marble rock
like examples for a definition?
sage python
So I'm thinking like, okay if instead of having this like, a bit of Rudin, a bit of this other analysis book that wasn't good, messy lectures, we had to teach ourselves linear algebra out of Hoffman-Kunze and do 20-30 (on one occasion 50) problems on top of our analysis pset
stray veldt
looked at his paper
sage python
Like that was kinda overwhelming
stray veldt
"oh, it seems i dont really understand my own argument anymore, so lets make it an exercise and skip it for now"
marble rock
damn i didnt know profs went througfh this shit
quartz pawn
lmao, I've heard of profs like this.
sage python
But like, okay that was twice as hard as a class which would just go through Rudin 1-7 in 10 weeks and assign 3/4 of the problems
And a class that's half that hard feels legitimately doable
quartz pawn
One of my professors said he had a prof who would sometimes realize in the middle of the lecture that his own argument wasn't exactly correct and would just sit there at the board and try to figure it out.
sage python
You'd need to dedicate quite a lot of time to such a class
quartz pawn
And it didn't help that he would just write whereever there was free space.
stray veldt
it happens
sage python
But it could be done
stray veldt
it happened to me once 5 mins before a seminar talk
quartz pawn
It's just funny because apparently the guy is brilliant; he just doesn't care about teaching.
lol
but when you're a professor, that's part of your job.
sage python
The second and third quarters of my analysis class were also quite tough but I felt they were fairly reasonable. They covered different things for sure
stray veldt
in intro courses you will have profs having no idea as well
marble rock
and is that normal?
stray veldt
that one semester i TAd intro discrete and the prof knew nothing about graph theory
he taught it himself
marble rock
thats me
sage python
But if I had to guess what it would be like if the guy teaching the second quarter of that class had taught the first, I'd say it was basically what I have in mind for a 10 week Rudin 1-7 class
stray veldt
he was doing something and then accidentally proved cantor bernstein
quartz pawn
lol I had a prof who never taught discrete before teach discrete.
sage python
So yeah
stray veldt
which does not really fit into intro discrete
sage python
"Whoops"
quartz pawn
He did a decent job but he even told us straight up that his abiilty to count i.e. combinatorics wasn't great.
The guy does work in PDE's
marble rock
same
speaking of PDEs ir eally wonder what the hype about for
every1 saying ' the theory of pdes is INSANELY deeep'
really wanna learn this shit for funs
like what does deep mean anyways
sage python
There's a lot going on in PDE tbh
stray veldt
probably they are saying it because the theory is deep
quartz pawn
Gotta go into Analysis with LA under your belt if the class goes into Multidimensional analysis.
marble rock
yea i am super curious
stray veldt
then do analysis first lmao
marble rock
yea hahaa
quartz pawn
Don't want to even waste time learning the required LA.
marble rock
like i really see werid words and concepts
sage python
Like you use a lot of tech from analysis at times
sage python
In particular functional analysis
marble rock
and surfaces
sage python
And yeah oftentimes you're solving PDE on manifolds, and the existence and properties of various solutions to the PDE are controlled by the underlying topology/geometry
stray veldt
my uni will have a focus on PDEs
in like a year or so
but hopefully im done by then
marble rock
im really interested
marble rock
and i dont know how unabstract math can be
i just learnt about tensor products
and like]
thats just abstract shit for me
regarldess fun or not
is there math that is not abstract
stray veldt
sure
marble rock
whats cool about it then
stray veldt
whats cool about abstractness
quartz pawn
Like if you want concrete examples just get one of those books like "applied ____"
marble rock
damn
stray veldt
just take a numerical analysis class
quartz pawn
Or that.
stray veldt
or stochastics or sth
i took both at some point
numerical analysis is the worst
stochastics is actually kinda cool
marble rock
like things which are abstract tend to like form connections alot
and the connections are always magic
quartz pawn
@sage python was that analysis class an undergrad class?
marble rock
and its just so weird
stray veldt
lmao
marble rock
category theory from scartch seems like magic on its own
wdym something in cat a can be something else in cat b
wt
wtf
stray veldt
undergrad cat theorist in the making
quartz pawn
lol.
marble rock
two things defined in two very seperate ways with diff philosophies and motivations
and they are the same in some way lmfao
marble rock
yea and im jsut saying its magic for me
flint forge
one of them anyway
stray veldt
you just abstract away everything, until it looks the same
stray veldt
i dont know, is it?
marble rock
idk
sage python
@quartz pawn yeah
quartz pawn
Like I feel like what is the point of making a class that hard.
marble rock
as i told u i know 0 cat theory
flint forge
no more honors analysis talk
marble rock
so if i say stupidi shit haha idk
flint forge
its been 3 years dami
quartz pawn
lol
sage python
That particular thing was a bit over the top
marble rock
yea i remember dami likes to talk on how hard the analysis shit was and how big the pset was
sage python
But my point was that because of it
flint forge
anyway category theory does reveal deep connections
its not just pointless abstraction
sage python
I think Rudin 1-7 in 10 weeks is doable
marble rock
yea and i really wanna know how
and why
but i mean i wont understand the connections if i dont know the objects connected
so yea
marble rock
what
marble rock
yea
flint forge
ALTHOUGH!
marble rock
what
flint forge
i do think the new txtbook
marble rock
yea ic ouldnt find it
flint forge
category theory and topology
marble rock
i was super interested but i couldnt find it
flint forge
is very good
quartz pawn
max has had very good things to say about that book since it came out a few weeks ago lol.
I would like to read it.
stray veldt
i agree without having seen that book
quartz pawn
I need to know top well though.
stray veldt
because that is how my topology class was taught
flint forge
I skimmed all of it in one sitting
marble rock
i dont thbink its meant for like beginners so yea
flint forge
it is
flint forge
its a first introduction to both topology and category theory
flint forge
there should be a pdf afaik
marble rock
where is it
marble rock
can you mention the author?
quartz pawn
ONe sec.
quartz pawn
It's open access
marble rock
googling top and category theory is bad
flint forge
"Topology: A categorical approach"
flint forge
marble rock
so should i use it for topoloyg?
flint forge
https://topology.mitpress.mit.edu/
I think its the best way to learn point set with an eye toward AT
quartz pawn
Algebraic Topology?
flint forge
yes
stray veldt
this looks a lot like my intro top
we did filters for the sole purpose of proving tychonoff as well
and the pset introduced nets
(for no particular reason)
marble rock
i got it
cool af
i think im suitable for the ug category theorist personna
literally ahs everything i have
stray veldt
that's not a good thing
marble rock
impaired problem solving
no free will
superiority complex despite nopthign to show it
no longer creative
sage python
yall got any more of them pixels
tribal kernel
When it comes to algebra books
I actually like Aluffi
Someone told me this channel makes fun of that book a lot though
marble rock
yup
sage python
Mostly that my pinned post doesn't paint it in a good light
marble rock
the one typing rn actually
sage python
I helped a friend at another school who was taking a class through that book and didn't like the problems at all
tribal kernel
What's wrong with the problems?
sage python
It felt like his logic in writing problems was basically "Yeah I don't feel like writing this part of the theory out I'll just break it up into a bunch of problems for the student to write up"
That union mostly straightforward ones
tribal kernel
Hmm I see
sage python
I'd prefer more problems which are hard by virtue of being harder to think of
Rather than just long
tribal kernel
I've done most of the chapter 1 and 2 problems and haven't had much difficulty with them. Maybe that will change as the book goes on but we'll see
sage python
It's somehow possible that my friend's prof just zoomed in on the worst of Aluffi's problems but I've seen the same sentiment elsewhere
valid moth
@sage python that's what she said
sage python
lmfoa
sage python
Archsys I should tell you about my Among Us run last night it was fucking insane
I made the ballsiest plays ever
flint forge
Arch this was your worst joke
Im normally a supporter
But thats what she said is so played out
That you have to use it only when it works perfectly
valid moth
okay look i'll be honest i wasn't even thinking about if it was funny or not i just identified several triggers for a potential joke and then made it
sage python
Anyway yeah that and Namington has said that Aluffi is slower than D&F which is just...
flint forge
Bad
tribal kernel
Dummit I find is best to be used as a reference text or encyclopedia of algebra
sage python
Max do you also know Among Us? If so come to chill and hear the story
tribal kernel
Not a main driver for a class
flint forge
Ive never played
Most textbooks are best as references imo
Hard to beat a good clas
Class
gray gazelle
who doesnt
tribal kernel
Except in algebraic topology. Both of my professors for that have been kinda bad lol
marble solar
My problem with 10 weeks of Rudin is the long term memory is shot
I prefer to cover things in great detail
Give motivation, add examples, play around etc.
Baptism by fire with Rudin likely just turns ppl away from Analysis
And stretch it out over time so that it sticks
So let's say you work on it for 3 months like chapters 1-5
Take a break, learn some other math
Go back for chapter 6-9
Plus, I may be partial because in particular I'm not very good at short fast sprints through material
Everything good I've ever done in math has been because I've had ample time to really think things through at
Slow & Steady wins the race
That, and I just hate Rudin with a passion
I tried Principles mehh, I tried his real & complex and it's just lukewarm at best
Ppl say his functional is good, but I'm getting more & more skeptical
marble solar
Just do Munkres chapters 2-4
limpid gazelle
I feel like munkres is too wordy
quartz pawn
There's this one book called A Course in Point Set Topology and it's like 154 pages
by John B. Conway
marble solar
That's about how long munkres chapter 2-4 is
I think munkres is the gold standard for a reason
He does the best job
quartz pawn
I guess so.
I mean like, it's a real short book for undergrads so it might not be what he's looking for.
I don't know of this other Conway book.
limpid gazelle
Oh that book is way too short
I already know like all the stuff in there
Kind of
Maybe I should continue munkres
quartz pawn
You could probably do lee but that's about manifolds.
yea Munkres is probably the best bet.
marble solar
No one really likes point-set
But ya just gotta get it done
I met a topologist who did current research in point-set
gray gazelle
quartz pawn
Lmao I've seen this.
I've seen all of the math ones I think.
This one and the complex analysis one are the best.
flint forge
is munkres a gold standard
id say like
a decent amount of the content is kinda unbased
gray gazelle
Munkres seems to get recommended a lot
quartz pawn
That was the book that one of my professors said that he used and he's a toplogist.
flint forge
it might well be better than some others but i dont think anyone actually likes munkres
quartz pawn
He said he didn't think it was all that great but it's the standard.
flint forge
which would make it not a gold standard
marble solar
Munkres is the gold standard for point-set topology
quartz pawn
Yea that's the impression I got.
marble solar
Just look at any qualifying exam that covers basic topology
They all recommend munkres
quartz pawn
Like it's the one book that kind of completely comprehensive but people think it may not be the best pedagocially.
flint forge
but its not a gold standard
a gold standard should be something which has little to no room for improvement
marble solar
Name a better point-set text
flint forge
thats also not an argument lol
i already said it might be better than alternatives
but its also kinda bad
quartz pawn
Like I guess it is "the standard". But like the "gold standard" entails more I guess.
Like "this is the quintessential example of what a Gen Top book should be"
flint forge
Like
tight crag
Seperation axioms are great
marble solar
Is it amazing no, but in the field of point-set topology there's nothing else that is as comprehensive, as rigorous, and as intuitive
flint forge
woke
well
i disagree
there are other books that are all of those things
maybe not intuitive
marble solar
In point-set?
tight crag
Tbh I think that there's a lot of material that algebraic topologists don't like
flint forge
what does 'as rigorous' even mean
tight crag
But that doesn't mean it's bad material
flint forge
point set is intuitive
except when it isnt
but when it isnt theres no way to make it work really
tight crag
I care more about point set topology than algebraic topology in my work lol
flint forge
thats because point set is set theory
Topology a categorical approach is a better intro imo if you care about doing AT
it is
marble solar
I mean Hausdorff did title his book Set Theory
tight crag
Which big shot set theorist?
flint forge
Hirschfeldt
he does computability + descriptive set theory + weird reverse mathematics
I mean idk what to tell you
marble solar
Appeal to Authority isn't an argument
flint forge
no its not
no he also means like
arithmetic hierarchy memes
and descrptive memes
unless you want to make point set its own beast
it bears no resemblance to modern topology really
marble solar
I mean there are modern point-set topologists
flint forge
sure
i don't
i mean at/difftop/htpy/geometric stuff/basically anything else
most throw out like the vast majority of spaces
before they even start working
you dont need to use CW for AT
most dont
marble solar
Does Hatcher?
flint forge
throw out most spaces?
marble solar
I only made it through chapter 1 of Hatcher
flint forge
or use CW
marble solar
CW
flint forge
no he doesnt
he uses them ofc
but he doesnt restrict
My point is that you can't say set theory and point set are too diferent
without acknowledging that point set
looks nothing like the rest of topology
flint forge
thats not really what the name means lol
anyway
you can disagree w the statement
but afaik point set topologists dont really describe themselves as topologists
marble solar
The one I spoke too called himself the true topologist
Since he was staying true to the foundations
dense pewter
imagine studying point-set topology
tight crag
Lol
marble solar
I thought that wasy funny
marble solar
Every joke has a little bit of truth
flint forge
point set was developed to formalize what topologists wanted to study
or at least what a group of people wanted to study
and then people just got rid of the ocunterexamples
hell most people are okay to stick w manifolds
tribal kernel
CW complexes and manifolds are sufficient for what most topologists I know want to study
flint forge
CW isnt a nice category even if they are your ultimate aim
sage python
CGWH
bleak canopy
@flint forge hi
how are you
also can you help me in #help-7｜zen1thxyz if you have time
steel viper
i thought CW category was important for homotopy reasons max
its "the homotopy category" or whatever
something something localization something something whitehead something something
flint forge
Uh
If you localize wrt whe
Then every space is weak equivalent to a CW complex
Therefore it works to just consider that subcategory
And most games work well up to htpy
But this isnt true if you dont pass to htpy
dense pewter
number fields up to homotopy
flint forge
Woke
dense pewter
also hi again sloth, and hi max I feel like we've sort of missed each other lately
tight crag
Lol sloth
flint forge
I always miss you
dense pewter
missed as in "haven't been present as the same time"
tight crag
Homotopy isn't that good of an invariant actually
flint forge
I know hahah
dense pewter
I'm responsible for teaching calc 2 to a class of 600 students (should have been much smaller but covid fucked things up) starting on monday
and I am N O T R E A D Y
flint forge
Holy shot
tight crag
I'm teaching calc 2 to a class of 45 students
flint forge
Do u have TAs
dense pewter
yes
tight crag
And it sucks
flint forge
How many
tight crag
I hate teaching online so much
dense pewter
5 grad students and 4 undergrads
tight crag
Is it online?
dense pewter
also 2 additional instructors who won't be doing lecturing
flint forge
Thats 60/instructor
dense pewter
just holding office hours and related things
dense pewter
yeah, it's not even that I have so many students because "diminishing returns" or something
it's also trying to manage all the course assistants
and deal with things like "the bookstore listed the wrong book for the course and students are complaining"
flint forge
Oh god
tight crag
Yeah I had that issue also
dense pewter
like... it's not my fault, I can show you the email where I told them what book to list and it's the correct one
("you" being my students)
in the past I would just tell "my boss" about these issues and let them deal with it but now I am "the boss"
hahaha
marble solar
Lay down the LAW
I took a topics course from a prof. who taught from his own notes that we had to buy for like 10 bucks. We didn't get it till like 8 weeks in when the term was almost over
marble solar
Because bookstore was dumb
dense pewter
hopefully prof gave you online copy or something
marble solar
He gave us PDFs for free as a token of goodwill
but I can't focus when I touch a computer
dense pewter
yeah I know what you mean
one thing I do like about this department is that there's always an "official" course textbook which is the most recent edition of stewart's calculus
marble solar
What text did you assign?
dense pewter
but then they tell all the students "this costs way too much, please just go buy a used copy of a previous edition for $10 off amazon, it is literally the same and costs so much less"
I did that ^
marble solar
lol
tight crag
My department uses the second edition always so you can just find a PDF online easily
marble solar
I think there was a prof. at Cal State Fullerton who wanted to use a different book than what the department mandated
dense pewter
"the bookstore was able to get the best deal on physical copies of the newest edition which is why we officially choose that but honestly just pick any old edition and you'll be fine"
marble solar
But the dept. chair had written the mandated book, and was making bank off of it
dense pewter
oof
dense pewter
I know in some cases like, departments will have contracts with publishers
marble solar
dense pewter
like "we'll use your book for the next x years in exchange for slightly cheaper copies" or something
and so if a prof was just like "ok everyone we're gonna use a different book instead" then that could actually be a problem
but in this case that's not what it seems like
marble solar
Yeah, this came out right when I was applying to transfer out of CC. I did not apply to Fullerton
Even though it was pretty close to home and cheap
civic carbon
I find it easy to give students options for texts but not require them for most courses.
marble solar
Zeta were you around for the Fullerton Fiasco above?
civic carbon
I was not
steel viper
htpy is a good invariant its just hard 
quick hornet
and was making bank off of it
was this ever established
if they had written and published it, i could see that
but i am unaware of anyone to "make bank off of" a textbook they wrote besides literally Stewart
quick hornet
but if they get $5 a purchase (which i'd say would probably be the "typical" commission for that price range)
theyre not really "making bank"
still feels exploitative dont get me wrong
dense pewter
so for the record I actually do think that stewart is a good calculus textbook for what it's trying to be (i.e. it's not trying to be spivak or apostol). I think it kind of gets buried under the fact that they come out with a new edition every 5 years and charge exorbitant prices for it
quick hornet
yeah dont get me wrong i think the textbook industry and its relationship with administrations is anticonsumer as fuck
dense pewter
and I think that a lot of institutions/classes don't use it to it's fullest potential. I was looking through it last year and it actually has really good problems and projects
yes I agree flami
gray gazelle
This is all a conspiracy by big textbook
quick hornet
also i know people teaching intro level courses often get pestered by textbook publisher reps
to use their specific book in their course
dense pewter
yeah I've heard that too
quick hornet
the fact that thats even profitable when i doubt more than, like, 10% of people are convinced by them
dense pewter
it hasn't happened to me... yet 
quick hornet
is pretty damn indicative of the profit margins on these books
yeah
and the textbook company needs to hire a rep
dense pewter
well I don't think instructors would really care that much in the end. like, you could probably just advertise "this book is cheaper than the competition and has better integration with whatever online course platform (like Canvas or Blackboard) you use"
quick hornet
i've even heard of profs being invited for lunch with a textbook rep but
i havent seen this in person lmao
marble solar
I've seen both in person
sage python
Jesus
dense pewter
the thing I don't get about stewart is like, how much content is in the book. I was looking through the "instructor's guide" for the textbook which I get access to cuz I have a faculty email address and like
marble solar
When I TA'd at my CC, a rep. from Pearson came to my professors office
We went out to lunch
dense pewter
for every section of the book it has a sample lesson plan with a suggested number of classes spent on that topic and if it's "required, recommended, or supplemental" material
quick hornet
yeah stewart has a SHITTON of money poured into it
to develop a really comprehensive support structure for profs
marble solar
I think the even worse offenders are mymathlab
dense pewter
and I added up all of the suggested number of classes for the "required" sections and like, the first 3 chapters was already longer than our full semester
marble solar
and mastering biology or mastering physics
quick hornet
it just feels really... manufactured
marble solar
Mastering chem. Those online platforms are really a money scam
quick hornet
like every class is gonna be different in how quickly it progresses, how the students take to concepts, what specific areas give difficulties, etc
dense pewter
yeah flami I know what you mean. I think that some resources are nice but I don't want to feel like they're teaching the class for me
quick hornet
i've TA'd linear algebra classes that instantly grasped the notion of an abstract field
gray gazelle
Man I remember those but I would have done them 15 years ago
dense pewter
like, they also literally have powerpoints made for each section
so you could just walk in class, put up the stewart calculus powerpoints, and just talk
quick hornet
and classes that took like 2-3 weeks before students were comfortable proving anything about an arbitrary field whatsoever
gray gazelle
The questions were just stupid formula plugging crap
quick hornet
the latter class wasnt necessarily "dumber" either, they both got through basically the same material over the semester
dense pewter
like I guess that makes it super easy but also that would be such a terrible class
quick hornet
just took longer on one particular section
sage python
Which section were they faster on?
marble solar
You know Texas Instruments did the same thing when they were promoting the 83's and 84's. Inviting teachers to "free training" gave them free calculators
came up with lesson plans for them to use it in
quick hornet
well dami they didnt progress in quite the same order so itss hard to say
dense pewter
oh god calculators
quick hornet
i will say that the latter class spent significantly less time on change-of-basis stuff
only like half a lecture
relative to 2-3
marble solar
I still don't know why HS requires calculators for calculus
quick hornet
but overall i think it was a bunch of small incremental things
more than one big timesave
dense pewter
because districts have deals with calculator manufacturers
marble solar
Other than TI can make money
gray gazelle
I find it funny my ti83plus from 2002 is still the same price
marble solar
Calc 1-3, linear algebra & diffy. q's at my CC ~ calculators were expressly forbidden
dense pewter
I think there are good arguments for using a calculator in a math class (although I don't do it) but like, just use a free online graphing calculator
desmos + wolfram alpha is all you need
mathematica if you're a real tryhard
yeah bookcrafty it's crazy
how it's like literally the same calculators for the past 20 years
same price
marble solar
Because the market demand has only increased
flint forge
The fact that my TI cant run sage 😔
quick hornet
partially that and also partially
theres no incentive to invest research funds in calculators
they already do evverything you need them to do
marble solar
They lobbied themselves to be the only exams usable on the ACT/SAT, AP Exams etc.
quick hornet
so people arent making more efficient/cheap/easy-to-manufacture microprocessors or wahtever
marble solar
I mean calculators
quick hornet
theres no need
marble solar
There's no incentive for them to do so
flint forge
My greatest life achievement is writing an integral estimator in labview
gray gazelle
They only win because it’s easy to check if students loaded stuff
sage python
Lol Max my prof for algebraic number theory is having us use computational programs for some problems
quick hornet
like if you look at the amount of money poured into r&d at any other tech company
sage python
He has one problem on the pset that's like "Use either Sage or something else to do blah"
dense pewter
I mean, that's not a bad idea dami
quick hornet
if you buy a cutting edge processor or gpu or whatever
dense pewter
I use sage pretty frequently
sage python
Yeah it's interesting for sure
"2b. Use sagemath or other computational algebra program to compute the discriminant and the basis of a ring of integers for the field K = Q(sqrt(7),sqrt(10)) from Milne's problem 2.6. (It is possible to do this by hand but I want you to get used to using computers to help with computations! You can install sagemath on your own machine or use it in the cloud at cocalc.)"
quick hornet
calculators are just really weird since no one cares about better callculators
since theres no reason to
civic carbon
Yeah, you really don't want to do much ANT by hand. Like calculating the ring of integers of Q(cuberoot(2)) even is a nightmare.
dense pewter
yeah
civic carbon
I did it, but it took an afternoon and I'm not sure I"m a better person for it.
dense pewter
I calculate rings of integers by "guess at what looks reasonable and then hope i'm right"
marble solar
Do you use computational programs for Analytic NT?
quick hornet
like realistically the main ways to actually improve a calculator are like
idk
making the screen bigger
lmao
and more colourful
thats about it
they already process shit fast enough
gray gazelle
Or switch to a tablet
dense pewter
I mean like, I would use desmos over a TI-XX any day
civic carbon
And I do a ton with character sums that end up requiring a lot of computation too.
quick hornet
yeah obviousily actual mobile devices that arent almost 2 decades old
civic carbon
usually just "is this character sum 0?"
gray gazelle
I mean 2008 iPhone would still beat the ti83
quick hornet
with how the size of flagship smartphones has ballooned recently
i wonder if theyll eventually eclipse high end TIs
in physical size
like theyre closer than youd think rn
lmao i just tried to take a photo comparing the sizes but then i realized my only camera is on my phone
the logistics of that dont work
gray gazelle
Lol
I have an iPhone se so it’s still way smaller
don’t need to carry a tablet in my pocket
gray gazelle
I don’t read on my phone, I mostly use it to tts books
hearty steppe
are there some more elementary linear algebra problem set books?
like ones more focused on application based problems like row echelon form problems and stuff like that and not so much proofs/analysis
hearty steppe
I am just trying to ease into linear algebra. I don't mind doing proofs/analysis problem sets when I'm ready for them but my understanding of proofs and analysis is not quite there and I am not trying to overwhelm myself
quartz pawn
You could try Jeffrey Holt's Linear Algebra and it's applications. It's a book that's filled with problems that we used in my first LA class.
And it's a pretty good book for an intro to LA. It introduces the invertible matrix theorem as "the big theorem" and through each chapter, as you learn about a new piece of LA, you add to your list of equivalent statements to where near towards the end of the book, you have all of them to give you IMT
hearty steppe
yea something on the level of a book like James Stewart calculus kind of problems.
scratch the surface, not too theory heavy
and like I said, its not that I'm not interested into getting into the theory heavy stuff. I'm still very new to that area of math.
@quartz pawn thanks, it looks a lot like Holt is what I am looking for right now
quartz pawn
Np
gray gazelle
There’s a schaum’s outline those are usually pretty applied
hearty steppe
Yea I’ll check that out too
pine maple
Does anyone know books or lecture notes with content similar to Diestel's Graph Theory but present in a simple ways with lot of figures and intuition?
brittle latch
maybe not exactly what you're looking for MIT has great open courseware lectures available for free
you could also just find books on zlib @pine maple
pine maple
hearty steppe
One of the easier ways to learn some intro graph theory is probably thru a discrete math book
ebon lantern
who wants to fight
sorry
read
ive been reading "until the end of time" by brian greene
balmy forge
books for engineering beginners?
i got the art of electronics bc EE seems cool, but i know so little about the other types i dont know
tribal kernel
Math for engineers or straight engineering?
balmy forge
straight engineering
i suppose i need to improve my math first
but for now i feel like i can at least get the basics downs b4 doing that
tribal kernel
Ah I’m not gonna be good for recommending that haha
long bear
I don't really have the current math tools in my toolbox to learn non-euclidean geometry properly, but are there any books that try to describe it to the layman?
Just to get a very distant feel for how it works
quick hornet
honestly if you have any analysis background i feel like you can investigate it yourself
meh maybe thats a bit presumptive
long bear
Interesting
shut grail
For the graph theory question, I recommend a book called introduction to graph and hypergraph theory
stray veldt
"HyperRogue"
shut grail
Voloshin
quick hornet
honestly i tried hyperrogue, it was cool but
it "felt" like a game that couldve taken place on a euclidean hex grid
just redrawn
the graphics rendering and stuff still helps with the intuition though
hasty turret
stray veldt
but hyperrogue uses poincare disk model afaik
quick hornet
it does yes
stray veldt
which is actually used by mathematicians
calm crane
ik books dedicated to 3 manifolds but you should prob learn some basic topology and diff geo first
i liked marden's intro to hyperbolic 3-manifold
long bear
that series is what got be quite interested
quick hornet
also im not a fan of the latter video
quick hornet
using locally euclidean geometry and calling it noneuclidean
long bear
oh
calm crane
iirc the person implemented like the nilgeometry too?
calm crane
or was it a diff one
quick hornet
i wouldnt call the earth a euclidean surface
but at the same time
idk, metrics all behave the same on that space except you have some fucky gluing going on
im not sure that counts
"morally"
it certainly counts definition-wise but meh
calm crane
small non0 curvature
stray veldt
also, this short introduction http://www.roguetemple.com/z/hyper/geoms.php might be understandable by a layperson?
quick hornet
talking about the second codeparade video btw, not hyperrogue
calm crane
im reading marteli intro to geo top rn that does go into some detail with the 8 geometries for 3-space seems quite good so far
quick hornet
i think hyperrogue is fine at what it tries to do
and can certainly help one build an intuition for hyperbolic geometry
white cradle
i can attest to that
it did help me build an intuition to some extent
but hyperrogue uses poincare disk model afaik
that's the default
it has many models to offer
oh for fucks sake
i missed the discussion by like 2 hours
fuck
long bear
lol
I did find a book called "An introduction to non-euclidean geometry" by David Gans
it seems to be quite accessible
white pebble
any recommendations for order theory ?
reef heron
so hype for hyperbolica
steel viper
ah yes my favorite book
haughty dove
I think there's some thick green standard books on lattice theory